A066077 a(n) is the number of x such that sigma(x)-1 is 0 or one of the first n-1 primes.

1, 2, 3, 4, 5, 7, 8, 10, 11, 14, 15, 17, 18, 21, 22, 25, 27, 30, 31, 32, 37, 38, 40, 43, 46, 48, 49, 51, 53, 54, 56, 58, 60, 61, 63, 64, 66, 67, 68, 74, 75, 79, 81, 86, 87, 88, 89, 90, 93, 96, 97, 100, 107, 108, 114, 115, 117, 120, 122, 123, 124, 125, 128, 130, 134, 135

Offset: 1

Author

Labos Elemer, Dec 03 2001

Keywords

• nonn

Comments

Former name was: Smallest x such that p(n) = Sigma[x] - 1. That did not match the Data. See A296375 for that sequence.

Links

• Iain Fox, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A000040, A000203, A058339, A058340, A066071, A066072, A066073, A066074, A066075, A066076, A066077, A066080.

Programs

Maple

N:= 100: # To get a(1)..a(N)
P:= ithprime(N-1):
S:= select(t -> isprime(t) and t <= P,map(-1+numtheory:-sigma, [$1..P])):
T:= Statistics:-Tally(sort(S),output=table):
ListTools:-PartialSums([1,seq(T[ithprime(i)],i=1..N-1)]); # Robert Israel, Dec 27 2017

PARI

first(n) = my(res = vector(n), a = 1); res[1] = 1; for(k=2, n, for(x=1, prime(k-1), if(prime(k-1) == (sigma(x) - 1), a++)); res[k] = a); res \\ Iain Fox, Dec 28 2017

Formula

a(n+1)-a(n) = A066075(n).

Extensions

Edited by Robert Israel, Dec 27 2017